Only showing world texture, not allowing to add texture to other objects
For the blender internal:

You have to change the texture type. The button is in the texture panel of the properties window. It is highlighted in red in the image below. You will want it to me set to Material Textures, the second button. A object that can have a materiel must be selected. If everything is selected or nothing is selected that option will not be there.



For Cycles:  

The texture must be added through the cycles material. The texture panel when using cycles behaves differently then in the blender internal. If there is a texture node in the selected materiel then the texture will display in the texture panel.